Do Gun Buybacks Save Lives? Evidence from Panel Data

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1 Do Gun Buybacks Save Lives? Evidence from Panel Data Andrew Leigh, Research School of Economics, Australian National University and Christine Neill, Department of Economics, Wilfrid Laurier University Send correspondence to: Christine Neill, Department of Economics, Wilfrid Laurier University, Waterloo, Canada; In 1997, Australia implemented a gun buyback program that reduced the stock of firearms by around one-fifth (and nearly halved the number of gun-owning households). Using differences across states, we test whether the reduction in firearms availability affected homicide and suicide rates. We find that the buyback led to a drop in the firearm suicide rates of almost 80%, with no significant effect on nonfirearm death rates. The effect on firearm homicides is of similar magnitude but is less precise. The results are robust to a variety of specification checks and to instrumenting the state-level buyback rate. JEL (I12, K14) 1. Introduction Following the 1996 massacre of thirty-five people in Port Arthur, Tasmania, the Australian federal government persuaded all states and territories to implement tough new gun control laws. Under the National Firearms Agreement (NFA), firearms legislation was tightened and made We are grateful to Juan Baron, Philip Cook, Jean Eid, Azim Essaji, Ana Ferrer, Francisco Gonzalez, Jens Ludwig, Alex Tabarrok, Justin Wolfers, editor John Donohue, an anonymous referee, and seminar participants at the Australian National University, the Research Institute of Industrial Economics, the University of Calgary, the University of California-Berkeley, the University of Melbourne, the University of Michigan, the University of Wisconsin-Madison, and the Association for Public Policy Analysis and Management 2008 Fall Conference for valuable advice and comments on this paper, and to Jenny Chesters, Susanne Schmidt and Elena Varganova for outstanding research assistance. All errors are ours. American Law and Economics Review doi: /aler/ahq013 Advance Access publication August 20, 2010 The Author Published by Oxford University Press on behalf of the American Law and Economics Association. All rights reserved. For permissions, please 509

2 510 American Law and Economics Review V12 N ( ) more consistent across all states and territories. As part of the NFA, it became illegal to hold particular types of firearms, in particular certain long guns. Guns that were no longer legal were subject to a government buyback, with owners being compensated for their newly illegal firearms at market prices. 1 In terms of the absolute numbers of guns destroyed, Australia s gun buyback ranks as the largest destruction of civilian firearms in any country over the period (Small Arms Survey 2007, Table 2.10). Its effect was to reduce Australia s firearms stock by around one-fifth, more than 650,000 firearms.inunitedstatesterms, this would be equivalent to a reduction in the firearms stock of forty million firearms (Reuter and Mouzos 2003). Although some of the firearms that were handed in came from households with multiple firearms, survey evidence suggests that the buyback nearly halved the share of Australian households with one or more firearms. 2 Previous studies of gun buybacks have typically found that they have little effect on death rates or violent crime (see, e.g., Callahan et al. 1994, who studied the 1992 buyback in Seattle, WA; and Rosenfeld, 1995, who looked at the 1991 and 1994 buybacks in St Louis, MO). Compared with these studies, an investigation of the Australian gun buyback has three major advantages. First, its scale is significantly larger than most other gun buybacks. In absolute numbers, five times as many guns were handed in under the 1997 Australian buyback as were bought back in the United Kingdom s much-touted gun buyback in the same year. Since death rate data are typically quite variable, the effects of smaller-scale buybacks are unlikely to be able to be distinguished from random noise. Second, the fact that the policy applied across the nation meant that gun owners could not simply travel across jurisdictions to purchase a replacement firearm, as can occur in the case of the more limited buybacks typical in the United 1. We use the term buyback here, since that is the terminology used in Australia. The program differed from what have been called buyback programs in the United States, however, where buyback programs have typically not been accompanied by a ban on the firearms bought back. 2. We have been unable to locate reliable evidence on the share of Australian households that owned a gun in 1996, immediately prior to the buyback. The best data appear to come from the International Crime Victim Surveys (ICVS), which indicate that 15% of Australian households owned a firearm in 1992, compared with just 8% in 2000.

3 Do Gun Buybacks Save Lives? Evidence from Panel Data 511 States. And third, the ability of an island nation to restrict illegal gun imports, coupled with the absence of any domestic gun manufacturers producing for the retail market, meant that legal restrictions on gun ownership were more likely to bite in Australia than would be the case in countries with porous land borders. 3 Although researchers have studied the Australian firearms buyback, most of these studies have looked only at time series variation. This approach suffers from the problem that the control group must be inferred from past time trends. If a time-specific shock affected homicide and suicide rates at the same point as the firearms buyback, it will be impossible for time series approaches to disentangle the policy change from the shock. By contrast, our approach in this paper exploits variation both across states and over time. The cross-state variation arises from different rates of firearm buyback in different states. Specifically, we ask the question: did firearms death rates decrease more substantially in states where more guns were bought back? To preview our results, we find that the withdrawal of 3,500 guns per 100,000 individuals reduced the firearm suicide rate by close to 80% and had no statistically significant effect on non-firearm death rates. Estimates of the effect on firearm homicides are less precise, but point estimates suggest that the firearm homicide rate also dropped by a substantial proportion. These results are robust to the inclusion of statespecific controls and time trends, to allowing for breaks in the statespecific timetrends,toflexible modeling of the dynamic impact of the NFA, and to using instrumental variables techniques to allow for potential endogeneity in the state-level gun buyback rate. This paper therefore provides evidence that reduced access to firearms lowers firearm death rates and may also lower overall death by suicide and homicide. The remainder of this paper is structured as follows. In Section 2, we briefly discuss the international evidence on firearm availability and violent deaths, as well as some of the methodological issues involved in estimating this relationship. Section 3 outlines the institutional details of the Australian firearms buyback and shows national-level trends. 3. Reuter and Mouzos (2003) raise this point and provide an extensive discussion of the background to and details of Australia s NFA, as well as a preliminary evaluation of its effects.

4 512 American Law and Economics Review V12 N ( ) Section 4 presents our cross-state empirical strategy and results. The final section concludes. 2. Evidence on the effects of firearm availability on violent deaths 2.1. Firearm possession and deaths The relationship between firearms ownership rates and violent death rates is one of the most hotly contested issues in the economics of crime. From a theoretical standpoint, gun control could either increase or reduce violence, depending on the particular circumstances (Marceau 1998). One set of hypotheses suggests that the relationship should be positive: more guns in the hands of criminals increase the probability that an assault will end in death, while the presence of guns in a home raises the chance that a suicide attempt will be successful. But another set of hypotheses suggests a negative relationship: more guns in the hands of law-abiding citizens may have a deterrent effect, which might in turn reduce the overall incidence of violence. 4 Cook and Ludwig (2006) provide a comprehensive review of the empirical literature regarding the mechanisms by which firearm ownership may affect death rates. Thereareanumberofstudiesthathave found a positive relationship between firearms ownership and firearms deaths using variation across countries or across regions within a country (e.g., Killias 1993). However, it is possible that this does not reflect a causal pattern (Duggan 2001). Cultural, legislative, or socio-economic factors in particular jurisdictions could explain both high gun ownership rates and high firearm death rates. A more compelling empirical approach is to use panel data. Under this approach, any factors that differ across jurisdictions and remain fixed over time can be controlled for by including jurisdictional-specific fixed effects in a multiple regression model. Similarly, any time-varying factors that affect all jurisdictions in the same way can be controlled for using time-specific 4. Duggan (2001) cites various estimates on the number of U.S. gun owners who successfully defend themselves from criminals each year: ranging from 75,000 to more than one million.

5 Do Gun Buybacks Save Lives? Evidence from Panel Data 513 fixed effects. Again, such approaches have been used at the sub-national and cross-national levels. Miller et al. (2005) find that reductions in firearm ownership rates across U.S. states are associated with declines in firearm suicide rates. Across a panel of 13 countries, Ajdacic-Gross et al. (2006) estimate a random effects model and similarly find a positive relationship between the share of firearms-owning households and the proportion of suicides committed with a gun. While these models can control for differences in death rates that are fixed geographically or in time, without a fuller causal model of death rates, they cannot account for correlations that arise between firearm availability and death rates that are caused by a third factor. For instance, a drought may lead to both increased firearm purchases to deal with wildlife encroaching on farmland and higher suicide rates of farmers due to increased bankruptcy. Or an exogenous rise in drug trafficking could lead to increased purchases of firearms by worried householders and increased homicides due to gang-related conflict. Beyond this, many other socioeconomic variables have also been found to affect suicide and homicide, and it is quite plausible that these same factors might affect firearms purchases. 5 Such factors may be unobservable to the econometrician. Moreover, there is little agreement in the literature as to an appropriate empirical model of either homicide or suicide rates, making it difficult to be sure that all relevant socio-economic factors have been addressed and therefore that estimates of the effect of firearms availability on death rates reflect a causal relationship. Further, it may be the case that places with both high firearm ownership and high firearm death rates have relatively low homicide and suicide deaths by non-firearm methods. This suggests substitution between methods; in other words, firearms are used in homicides and suicides in places with 5. Among the factors that have been found to affect suicide rates are New Deal spending (Fishback 2007); the divorce rate (Gruber, 2004); divorce laws (Stevenson and Wolfers, 2006); the violent crime rate, the Vietnam War, and the share of the population aged (Cebula and Zelenskaya, 2006); business cycles (Varen 2004); alcohol use (Carpenter 2004); unemployment rates and permanent income (Hamermesh and Soss 1974); and urbanization rates (Neumayer 2003). Factors correlated with homicide include inequality and poverty, percent of the population that is urban, is resident in female-headed households, or has recently moved (Cook and Ludwig 2006); and male youth unemployment rates and average weekly earnings (Narayan and Smyth 2004).

6 514 American Law and Economics Review V12 N ( ) high firearm ownership rates simply because the firearms are available. In the extreme case of complete method substitution, access to firearms has no impact on the number of violent deaths, merely the method by which those violent deaths occur. From a policy standpoint, this is clearly an important question, yet pure cross-sectional or time series methods are unable to separate out these effects. Another concern is the accuracy of data on firearm availability. Duggan (2001) notes that a lack of reliable data on gun ownership makes many of these studies rather difficult to rely on. He uses subscriptions to gun magazines (which he shows are closely correlated with firearm ownership) as a proxy for firearm ownership. Cook and Ludwig (2006) and Bridges and Kunselman (2004) use the percentage of either suicide or accidental deaths that are due to firearms as a proxy for firearm availability. All three found that a higher (estimated) firearm availability rate was associated with higher firearm homicide rates. Finally, the results from such studies may be contaminated by the endogeneity of firearm ownership. For example, in jurisdictions with higher rates of violent crime, individuals may be more likely to own a firearm to protect themselves. In this case, firearms ownership may merely reflect current crime rates or expectations of future crime rates. In order to identify the causal effect of access to firearms on deaths, it is preferable to exploit some exogenous source of variation in firearms ownership rates Firearm regulation and deaths Perhaps one of the most promising avenues for identifying such exogenous changes in access to firearms is to examine the effects of changes to firearm legislation and regulations. Some caution is required in attributing changes in regulation to changes in access to firearms, since the degree of enforcement may be equally important. Indeed, it is possible that stricter legislation may not in fact reduce firearm access in the absence of enforcement. Another issue is that legislative reforms often include a package of measures which can make it difficult to separate, for example, regulations on ownership from rules governing the proper storage of firearms.

7 Do Gun Buybacks Save Lives? Evidence from Panel Data 515 There have been a very large number of studies of tighter firearm legislation or other related policy changes on death rates. We cannot carry out a comprehensive review of the entire literature here. The majority of these, however, rely mostly on time series methods including studies of the 1977 Canadian gun control legislation (Leenaars and Lester 1996; Carrington 1999) and of the 1994 U.S. federal assault weapon ban (Koper and Roth 2001a; see also Kleck 2001; Koper and Roth 2001b). These studies tend to find some evidence of a decline in firearm-related deaths following the passage of tighter gun control legislation. Four existing papers study the effects of Australia s 1997 National Firearms Agreement on Australian firearm deaths. Chapman et al. (2006) take a purely time series approach to the question, arguing there is evidence of a decline in firearm suicides and perhaps in homicides after They also note that there were thirteen mass shootings in Australia during the period , but none in the decade Baker and McPhedran (2007) also take a simple time series approach. Their empirical findings are similar to those of Chapman et al. (2006), although their interpretation of the results is markedly different. Lee and Suardi (2010) estimate an ARIMA model and attempt to find a structural break in the time series process for firearm and non-firearm homicides and suicides at 1997 but find none. Ozanne-Smith et al. (2004) examine the effects of firearms legislation in Australia on overall firearm deaths, using two periods of policy change. The first was a tightening of firearms legislation in the state of Victoria, which occurred around 1988, preceding by almost a decade the more general tightening of legislation that occurred in the rest of Australia in Comparing firearm deaths in Victoria and the rest of Australia, they find that such deaths fell more rapidly in Victoria during the period and fell more rapidly in the rest of Australia from 1997 to They conclude that tighter gun controls led to a substantial reduction in firearmrelated deaths overall and in firearm suicides in particular. The results in that paper rely on the assumption that the NFA had no effect on firearm availability in the state of Victoria, which is not consistent with the evidence that substantially more firearms were bought back in Victoria than in many other states.

8 516 American Law and Economics Review V12 N ( ) A problem with studies of national gun control law changes that rely on time series variation is that it is impossible to distinguish between two factors, both of which may be important: (1) the effects of socio-economic or other policy changes on all suicides or homicides and (2) method substitution. 6 Unless it is possible to control for all conceivable timevarying shocks, it is not feasible to control for (1) and thus identify (2). An alternative approach is to exploit sub-national variation in firearms regulations. Since most countries regulate firearms at the national level, studies of this type have tended to use variation across jurisdictions within the United States. This has the advantage that crime statistics are more comparable, but the disadvantage that sub-national restrictions can be circumvented by buyers who are willing to travel interstate. The most studied regulatory changes have been the introduction of laws allowing concealed carry permits, shall-issue laws, and restrictions on youth firearm ownership. For example, Rosengart et al. (2007) found that the introduction of shall-issue laws, implemented in twenty-three states over the 1980s and 1990s, led to an increase in the rate of firearm homicide of one per 100,000 individuals, after controlling for state-specific differences in death rates. There have also been studies of U.S. firearm buybacks (Callahan et al. 1994; Rosenfeld 1995). These typically find the buybacks have little or no effect on death rates, but the programs evaluated are much more modest than the Australian NFA. Levitt (2004) includes changes in U.S. gun control laws over the 1990s as one of his six factors that do not explain declines in crime over the same period. He notes three reasons why gun buybacks in particular would not be expected to be effective: (1) the guns surrendered are those least likely to be used in crimes because they are surrendered voluntarily; (2) replacement guns are easily obtained; and (3) the typical buyback is relatively small in scale. We describe the NFA in the next section, but to anticipate these arguments: we argue that none of these factors are relevant to the Australian buyback; since the NFA involved a large-scale buyback of firearms, the buyback was compulsory in the sense that retaining possession of the firearms was illegal, and the guns could not be easily replaced with similar firearms. 6. For a more technical discussion of this problem, see the appendix to Neill and Leigh (2008).

10 518 American Law and Economics Review V12 N ( ) 3. Australian Firearm Regulation and Firearm Deaths 3.1. Trends in Australian Suicides and Homicides In the decade following the NFA, there has been a substantial drop in firearm deaths in Australia (Figures 1a and1b). Firearm suicides have dropped from 2.2 per 100,000 people in 1995 to 0.8 per 100,000 in Firearm homicides have dropped from 0.37 per 100,000 people in 1995 to 0.15 per 100,000 people in These are drops of 65% and 59%, respectively, and among a population of 20 million individuals, represent a decline in the number of deaths by firearm suicide of about 300 and in the number of deaths by firearm homicide of about 40 per year. At the same time, the non-firearm suicide rate has fallen by 27% and the non-firearm homicide rate by 59%. 7 It is also clear from Figure 1 that firearm deaths have been falling on a consistent basis in recent decades, while a similar trend is not as clear in the case of non-firearm deaths. 8 Firearm deaths both homicide and suicide are currently at exceptionally low levels by historical standards. The previous low in the rate of firearm suicide was in 1944, at 1.63 per 100,000. The firearm suicide rate has been below that level since The firearm homicide rate is considerably more volatile, but for the years 2004 to 2007 it has been recorded as at or below 0.15 per 100,000 people. It has dipped below 0.2 per 100,000 on only one other occasion, in Non-firearm suicides, on the other hand, have remained relatively high compared to historical averages, despite declines in the early 2000s. The increase in non-firearm suicides from 1996 to 1998 is noteworthy, since some commentators (for instance, Baker and McPhedran 2007) have pointed to this as possible evidence of substitution from guns to other 7. There are concerns that data on external causes of death may be affected by changes to collection methods in 2002 (AIHW 2009), leading in particular to a decline in deaths categorized as self-harm (suicide) and an increase in deaths that are identified as due to external causes of undetermined intent. 8. Note again that there may be some inconsistencies in the homicide (death by assault) statistics after The figures for 2004 and 2005 seem exceptionally low and do not align with the justice statistics on homicides in those years. See Chapman et al. (2006). Recently released data from 2006 and 2007, however, do appear to be consistent with the figures from 2004 and Again, however, this may reflect an inconsistency in the data.

11 Do Gun Buybacks Save Lives? Evidence from Panel Data 519 methods of suicide following the gun buyback. Non-firearm homicides havelikewiseremainedrelativelyhighcomparedtolong-runhistorical averages, although they appear to have dropped sharply since The National Firearms Agreement Following the April 1996 Port Arthur killings, the Australasian Police Ministers Council achieved agreement between federal and state governments to toughen and harmonize firearm laws across Australian states and territories. The key element of the NFA was the ban of the sale, importation, or possession of particular types of previously legal firearms mostly automatic and semi-automatic long arms. A buyback scheme was implemented to compensate owners for the compulsory forfeiture of any newly illegal weapons. Reuter and Mouzos (2003) state that the agreement effectively introduced uniform licensing and registration of firearms in all eight states and territories of Australia, replacing a patchwork that included regimes of varying stringency. Moreover, certain classes of weapons (self-loading rifles, self-loading and pump-action shotguns) were prohibited, as was the importation of these weapons. To encourage compliance with the new prohibitions, the federal government financed a large-scale gun buyback program, conducted by the states. The buyback initially covered only newly prohibited weapons, primarily long arms; later it was extended to include nonconventional weapons, such as submachine guns and heavy machine guns. There was also an amnesty for handing in unlicensed firearms during that same period, but no payments were made for these weapons (p. 129). 10 Prices were centrally determined by an expert committee, based on the retail price of the firearm, and did not vary across states. Altogether, almost 650,000 prohibited firearms were bought back during the initial amnesty. Substantial numbers of non-prohibited but unlicensed firearms were also handed in. 11 Although it is difficult to be certain, due to the unreliability of survey data on gun ownership, Reuter and Mouzos (2003) state that this 10. The distinguishing feature of self-loading and pump-action weapons is that they do not require the user to insert fresh ammunition after each pull of the trigger. 11. For NSW, Australia s most populous state, Reuter and Mouzos (2003) were able to obtain data on the number of non-prohibited firearms that were handed in. In that state, 37,000 non-prohibited firearms were handed in, for no compensation. That figure was 24% of the 156,000 prohibited firearms handed in to NSW authorities.

12 520 American Law and Economics Review V12 N ( ) most likely constituted a withdrawal of around 20% of the total stock of firearms from the community. It is extremely unlikely that this withdrawal of firearms could have beenquicklyreversedinaustralia.therearenodomesticfirearms manufacturers, so that all firearms must be imported into the country. Records from the Australian Customs Service show that in the 3 years prior to 1996, Australian firearms imports averaged around 50,000 per year, of which about 25,000 were rifles. After the buyback, average imports fell to about 30,000 per year, of which 10,000 were rifles. Thus, if anything, there appears to have been a slowdown in imports after Although the available data are incomplete, it appears that law enforcement agencies were responsible for a large percentage of overall purchases. For example, one source indicates that more than one quarter of all handguns purchases in the period were by law enforcement. Even if we made the extreme assumption that all imported firearms were added to the civilian firearm stock and no firearms were ever destroyed, at current import levels of 30,000 per year it would take around 20 years for the civilian firearm stock to recover to pre-buyback levels. Publicly available data on imports by state suggest there may have been a slight negative relationship between subsequent imports of firearms per capita and the buyback rate that is, states with a high buyback rate also saw somewhat lower growth in firearm imports. This relationship is not, however, statistically significant, and we do not have information that allows us to separate out civilian purchases from law enforcement and military purchases, so we cannot be sure that this reflects primarily civilian purchases. Although the NFA buyback targeted firearms that were of the type that had been commonly used in crimes, an important feature of the buyback is that very few of the firearms handed in to police were military-style automatic-fire weapons. For the state of Victoria (the only jurisdiction to provide a breakdown of the types of guns handed in), Reuter and Mouzos (2003) report that nearly half of the guns were.22 caliber rifles, and almost all the remainder were shotguns. Less than one in 1,000 of the weapons handed back in Victoria was an automatic. Further, given the very strict Australian legislation restricting access to hand guns, there was limited opportunity to substitute away from newly prohibited firearms towards other automatic or semi-automatic firearms.

13 Do Gun Buybacks Save Lives? Evidence from Panel Data 521 Table 1. Number of deaths and type of firearm used for homicides and suicides ( and ) Suicide Homicide Handgun Rifle/ shotgun Other/ unspec Handgun Rifle/ shotgun Other/ unspec (A) Number of deaths Rate per 1 million % of deaths 4.4% 70.5% 25.1% 7.5% 53.1% 39.5% (B) Number of deaths Rate per 1 million % of deaths 11.0% 71.6% 17.4% 20.8% 36.5% 42.7% Change in deaths (B-A) Change in # of deaths % change in death rate 18.1% 51.9% 67.3% 71.5% 57.8% 33.7% Source: Australian Bureau of Statistics, Cause of Death collection (data available on request). National statistics on firearm deaths separate deaths caused by handguns from those caused by long guns. 12 This is useful because the NFA applied primarily to long guns. Prior to the 1997 law change, handguns accounted for 4% of all firearm suicides and 8% of all firearm homicides (Table 1). Afterwards, the figures increased to 11% and 21%, respectively, largely because of a decline in deaths attributable to long guns. 13 Overall, 71% of suicides were with identified long guns, and the same was true of 53% of homicides. Of course, not all of the long guns used in these homicides and suicides would have been subject to the buyback, but the fact that the drop in deaths was larger among the type of firearm most affected by the buyback provides suggestive evidence that the NFA played a role in the fall in firearm deaths. The oft-heard claim that buybacks remove mostly low-risk guns (because only an individual who was not planning to use a firearm would hand it in) is typically based on U.S.-style buybacks which are 12. We were unable to obtain a reliable breakdown of firearm deaths by state by firearm type (which might otherwise have allowed us to estimate a triple-difference model). 13. Note that a tightening of handgun regulations was implemented in In general, this is thought to have been relatively ineffective compared with the 1997 NFA. However, the data do suggest that, after the 2002 law change, handgun homicides and suicides dropped more than did homicides and suicides using other firearms.

14 522 American Law and Economics Review V12 N ( ) entirely voluntary. It is more an argument about the characteristics of the owner than about the characteristics of the firearm. Such concerns have less force in the case of Australia s program, which was accompanied by a ban, than in the U.S. cases. In general, however, one might hypothesize effects in either direction. For example, if firearms owners were more likely to hand in a firearm if they had a depressed teenager in the house, the guns handed back might reasonably be described as high risk. Conversely, if an owner s probability of handing back a firearm is negatively correlated with his or her predisposition towards violence, the guns handed back might reasonably be described as low risk. Because the Australian buyback was both targeted at firearms that police and the government considered high risk and that had been relatively unregulated previously, and because the buyback was accompanied by a ban and other tightening of firearm regulations, we do not think it is reasonable to describe the program as having removed primarily low-risk weapons from the Australian community. This distinguishes it from programs in the United States, where such a judgment appears more reasonable. We have focused here on the buyback elements of the NFA. However, there were other elements of the NFA that may have led to a stronger tightening of firearm ownership legislation and enforcement in some states than in others. The most important of these were: that a national register of all firearms would be established (previously, not all states required registration of long guns); that there would be a requirement to give a valid reason for owning a firearm in order for an individual to be licensed (personal security was specifically excluded as a valid reason); that a permit would be required to purchase a firearm, with a required 28-day waiting period; and the introduction of storage and safety standards. 14 To the extent that states that had initially high firearm ownership rates did so because of weaker legislation surrounding, say, sale or licensing, the NFA may have had two effects: first, to reduce the number of firearms held per capita and second to impose more stringent legislation. There is evidence that states with higher initial rates of gun ownership (including 14. A more complete description of the legal changes associated with the NFA is provided by several sources, including Reuter and Mouzos (2003).

15 Do Gun Buybacks Save Lives? Evidence from Panel Data 523 Tasmania and Queensland) had fewer legislative restrictions related to firearm ownership than other states (Reuter and Mouzos 2003). It is important to keep this possibility in mind when interpreting the results in this paper. Insofar as a higher buyback rate is associated with greater stringency in the overall regulatory and enforcement environment, our estimates need to be interpreted as the effect of the entire NFA policy package. In summary, the NFA led to consistent legislation across Australian states, required licensing of gun owners and registration of guns, and significantly tightened restrictions on the types of firearms that could be legally held. In focusing on long guns, the legislation covered the group of firearms that had been most commonly used in firearm suicides and homicides and in particular outlawed firearms of the type that had been used in recent mass shootings in Australia. Internationally, the gun buyback associated with the Australian NFA was the largest of its kind in recent decades, withdrawing one fifth of the stock of firearms from the community and likely substantially reducing the number of households possessing a firearm. 4. Empirical Strategy and Results 4.1. Identification issues While the time series evidence suggests that the NFA reduced gun deaths (Ozanne-Smith et al. 2004; Chapman et al. 2006), it suffers from the lack of a credible control group or of a fully specifiedmodelofthe determinants of suicide and homicide. An alternative to developing a full predictive model of death rates is to use panel techniques, relying on variation in the intensity of the law changes associated with the NFA at the sub-national level. Due to administrative limitations, the finest geographic level for which we are able to obtain buyback data is the state and territory. 15 Australia has six states and two territories. Data on the number of firearms bought back in each jurisdiction were provided to the federal Attorney-General s department by each of these jurisdictions and are tabulated in Reuter and 15. We inquired to see whether it was possible to obtain buyback statistics for smaller geographic units, but the Attorney-General s Department (which collated statistics on the buyback) advises that such data do not exist in any systematic form.

16 524 American Law and Economics Review V12 N ( ) Table 2. Guns collected by state Total guns collected Guns collected per 100,000 residents Gun ownership rate (SE) Victims in Port Arthur massacre Australian Capital Territory 5,246 1,698 0 New South Wales 155,774 2, (0.009) 6 Northern Territory 9,474 5, (0.067) 0 Queensland 130,893 3, (0.016) 0 South Australia 64,811 4, (0.022) 2 Tasmania 34,584 7, (0.050) 12 Victoria 207,409 4, (0.011) 12 Western Australia 51,499 2, (0.022) 1 Total 659,690 3, (0.006) 33 Guns collected data are from Reuter and Mouzos (2003). Resident calculation is based on 1997 population. Gun ownership rate is the share of households with a firearm and is estimated from the 1989 and 1992 International Crime Victim Surveys. These surveys did not contain a separate designation for residents of the ACT, though Harding (1981) estimated that in the , the gun ownership rate in the ACT was Mouzos (2003). These data are set out in Table 2, which demonstrates that the number of guns withdrawn per 100,000 state residents differed substantially across Australian states and territories, ranging from a low of 1,698 in the Australian Capital Territory to a high of 7,302 in Tasmania. In this paper, we ask whether firearm deaths dropped proportionately more in states where relatively more firearms were bought back. If the gun buyback itself was effective in reducing firearm-related deaths, then this would imply that states where more firearms were removed from the population should have seen a greater reduction in firearm death rates than the Australian average. Because we are comparing across states, we are able to account for time-specific shocks affecting all of Australia, something that is impossible using a simple time series approach. 16 This differences-in-differences approach relates changes in death rates to changes in states gun ownership rates (caused by different gun buyback rates). It assumes that all Australian states and territories would 16. This approach is similar to that taken by Ludwig and Cook (2000), in evaluating the effects of the Brady Handgun Violence Prevention Act in the United States, which required all states to implement a system of background checks and waiting periods for the purchase of handguns from licensed dealers. They ask whether death rates fell more in states that did not already meet the new federal requirements than in states that already had at least as stringent a system of checks in place and find little evidence that death rates fell as a result of the Brady Act.

17 Do Gun Buybacks Save Lives? Evidence from Panel Data 525 have had the same change in death rates if they had experienced the same change in firearms ownership. If states with higher initial firearm ownership rates also had weaker firearm legislation or enforcement and if the NFA led to a reduction in the relative weakness of the legislation and/or its enforcement, then any estimated effect cannot be interpreted purely as the impact of the buyback. Rather, it will be the result of both the removal of firearms and the tightening of firearms legislation and enforcement. A second assumption in using this identification strategy is that the buyback rate in each state was exogenous, in the sense that it was not the result of preexisting trends at the state level. 17 We do, however, show that allowing for a national or state-level trend break beginning in 1988 the time at which the decline in firearm homicides and suicides appears to have begun does not affect our qualitative results and that to the extent that there is any evidence that preexisting trends may bias our results, it would tend to bias our results towards the buyback having a larger impact on firearms deaths. Implicitly, our strategy also ignores the possibility that firearms are transported across state boundaries prior to being handed in. Given that the compensation regimes were similar across Australia, we believe this is unlikely. To the extent that firearms were moved from one state to another, this will likely bias our estimates towards zero. For the purposes of our empirical strategy, what matters is that differences in buyback rates were not correlated with other factors that might have affected gun deaths. In particular, we are concerned about two potential confounders. First, if differences in buyback rates were driven by pre-existing gun ownership rates and if the relationship between gun ownership and gun deaths is non-linear, this could lead to a spurious correlation. However, although a non-linear relationship is theoretically plausible, we have been unable to locate any studies supporting such a theory. Second, our empirical strategy relies on the assumption that the statelevel gun buyback rate is exogenous with respect to firearms death rates. It is thus important to consider the various factors that might explain why the buyback rate varied across states. By definition, the overall buyback 17. National-level time trends are controlled by year fixed effects. We also include state-level linear time trends as a robustness check in all specifications.

18 526 American Law and Economics Review V12 N ( ) rate is equal to the rate of ownership of the newly illegal firearms multiplied by the compliance rate. To the extent that differences are driven by initial differences in firearm ownership rates, the withdrawal of firearms can be considered plausibly exogenous driven by the initial social norms, industrial composition, and laws in each state. To test this, we estimated the relationship between two proxies of state-level gun ownership rates in 1997 and the gun buyback rate. The first proxy is data on ownership rates of all types of guns taken from the 1989 and 1992 ICVS. Since the sample size at a state level is quite small, we pool data from both waves. This is likely to be a good proxy for gun ownership when the buyback commenced, so long as gun ownership rates did not change differentially across states in the period The second proxy, following Cook and Ludwig (2006), is the percentage of suicides in which a firearm was used. 18 Results are shown in Table 3. Ascanbe seen from the R 2 statistics, the correlations are very high. Over 60% of the state-level variation can be accounted for by each proxy individually, and the relationship is significant at around the 1% level. When both proxies are included in the regression, the high degree of correlation between the gun ownership rate and the percentage of suicides using firearms leads to each individual relationship being insignificant, but the combined effect of the two is statistically significant at the 5% level. These results strongly suggest that a very substantial proportion of the variation in the gun buyback rate was simply due to differences in prior gun ownership rates. Differences in compliance rates are nonetheless likely to play some role. Combining data from several sources, Reuter and Mouzos (2003) estimate that compliance was about 50% in Queensland and New South Wales, 70% in Victoria (the only state that previously required firearms to be registered), and 90% in Tasmania. Due to the paucity of data on firearm ownership rates prior to 1997, however, these estimates are imprecise. Differences in compliance rates would not be a concern if they were driven by factors unrelated to changes in death rates or if they were driven by factors that are controlled in our regression. For instance, farmers were more likely to be granted a license for a firearm than urban 18. We use the percentage of suicides undertaken with a firearm in Results are similar if instead we average over the years prior to the NFA.

19 Do Gun Buybacks Save Lives? Evidence from Panel Data 527 Table 3. Relationship between the gun buyback rate and proxies of firearm ownership Gun ownership ( ) 15,241 7,147 t-statistic (3.51) (0.94) p-value % of suicides that are firearm 15,092 24,480 t-statistic (1.27) (3.82) p-value Joint significance F 7.58 p-value R-squared Numbers of observations Dependent variable is the gun buyback rate at the state level. p-values are in italics, t-statistics in parentheses. We assume that the gun ownership rate in the ACT is the same as in NSW. Estimates are cross-sectional, showing the relationship between the state-level gun buyback rate, estimated gun ownership (as described in Table 2), and the percentage of all suicides in 1995 that were identified as with a firearm at the state level. residents, so that the less urban states would be expected to have had lower buyback rates. Since we include both state fixed effects and the percentage of the population in urban areas as controls, however, any such correlation will not bias estimates of the effect of the buyback rate on death rates. However, if the compliance rate was in part determined by factors that mayalsohavedrivendifferences in death rates across states, this could bias our estimates. It is also possible that the number of guns handed back varied according to the impact of the Port Arthur massacre on each state. The most direct wayinwhichstateswereaffected by the massacre was if a significant number of their residents were killed. If a large number of state residents were victims of the massacre, this might have led the state s mediato devote more coverage to the massacre and slanted public debate in the state in favor of the buyback. To the extent that states with more victims had higher rates of compliance with the buyback, this can be regarded as a valid source of variation (in the sense that it would only affect firearms deaths through its effect on the buyback). However, if it is also the case that a higher number of victims had a direct effect on the propensity of residents in that state to use a firearm for homicide or suicide, this would not be a valid variation (since it might affect firearms deaths directly). From the perspective of our empirical strategy, we would be

20 528 American Law and Economics Review V12 N ( ) concerned if exposure to the Port Arthur massacre affected social norms about gun use in a state, but not if it affected a state s gun buyback rate. The data do indeed show that states with greater exposure to the Port Arthur massacre had higher buyback rates (Table 2). We observe a correlation between the number of massacre victims and the number of guns handed back per 100,000 residents of 0.5. However, this relationship is not robust to also including the gun ownership rate in the regression. When we regress the buyback rate on both the previous gun ownership rate and the number of massacre victims, the former is positive and statistically significant, while the latter becomes insignificant, though the coefficient remains positive. As we have noted, this would be a valid source of variation, but it appears that relatively little of the cross-state variation in buyback rates was actually driven by states exposure to the Port Arthur massacre. We have been unable to find appropriate attitudinal data that would allow us to test the impact of the Port Arthur massacre on a state s social norms about gun use. However, two things can be noted about this. First, to the extent that the Port Arthur massacre affected social norms about gun use in a state, we believe that it is more likely to have affected gun homicides than gun suicides (since the event itself was a mass homicide). And second, such an impact would likely have faded out within a few years after the massacre. In our empirical results, we test this by separately looking at the effects of the buyback on firearm deaths in the short run and medium run. Another possibility is that some people kept their firearms in order to defend themselves against the threat of violence in the future. If individuals were able to correctly predict trends in future crime rates (including homicide), this could lead to a negative correlation between the number of guns handed back (as a share of the population) and the future change in crime rates. To address this, we use the same information that such a rational home defender would have had namely the past trendincrimerates. 19 If this defensive gun-use hypothesis is valid, we 19. The assumption that the general public forecasts future crime rates by using past trends seems reasonable to us, though we know of no empirical evidence on this point. In the U.S. context, Levitt (2004) shows that even experts appear to predict future crime rates through linear projection.

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